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rank of a Lie group

Coontents

Context

Group Theory

Lie theory

∞-Lie theory (higher geometry)

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Examples

\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras

Coontents

Definition

The rank of a Lie group is the dimension of any one of its Cartan subgroups, hence equivalently the dimension of any one of the Cartan subalgebras of its Lie algebra.

Properties

For compact connected Lie groups

For connected compact Lie groups then a Cartan subgroup is a maximal torus and hence in this case the rank of the Lie group is the dimension of any one of its maximal tori.

References

Created on January 10, 2017 at 11:08:56. See the history of this page for a list of all contributions to it.